Finite Group DatabasebetaFinite Group Databasebeta| order | 12928 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C2×C32×C101 ⋊ C2 |
| Sylow | C101 ⋊ #1401 |
72 conjugacy classes of subgroups.
| minimal degree | μ(G) = 165 |
| transitive degree | μt(G) = 6464 |
A minimal faithful permutation representation — 2 generators on 165 points:
(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25)(26,27)(28,29)(30,31)(32,33)(34,35)(36,37)(38,39)(40,41)(42,43)(44,45)(46,47)(48,49)(50,51)(52,53)(54,55)(56,57)(58,59)(60,61)(62,63)(64,65)(66,67)(68,69)(70,71)(72,73)(74,75)(76,77)(78,79)(80,81)(82,83)(84,85)(86,87)(88,89)(90,91)(92,93)(94,95)(96,97)(98,99)(100,101)(102,104)(103,110)(105,121)(106,124)(107,119)(108,117)(109,120)(111,134)(112,137)(113,132)(114,116)(115,133)(118,127)(122,145)(123,149)(125,152)(126,130)(128,146)(129,148)(131,140)(135,143)(136,158)(138,160)(139,151)(141,144)(142,157)(147,154)(150,164)(153,155)(156,162)(159,163)(161,165);(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,54,56,58,60,62,64,66,68,70,72,74,76,78,80,82,84,86,88,90,92,94,96,98,100,101,99,97,95,93,91,89,87,85,83,81,79,77,75,73,71,69,67,65,63,61,59,57,55,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(102,103,106,112,107,113,125,138,108,114,126,139,128,141,153,161,109,115,127,140,129,142,154,162,105,111,122,135,123,136,150,159)(104,116,118,143,119,144,147,163,117,133,145,137,146,157,164,160,120,134,124,151,148,158,152,165,121,110,130,131,149,132,155,156)Polycyclic presentation:
2^7,101|a^2=d,c^2=g,d^2=e,e^2=f,f^2=g,b^a=bc,c^b=cg,d^b=dg,h^b=h^1003256 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12928, 2651);